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#1 2024-09-09 02:30:13

harpazo65
Member
From: Brooklyn, NY
Registered: 2024-09-07
Posts: 52

Classifying Numbers

List the numbers in set B that are natural, integers, rational, irrational amd real.

B = {-5/3, 2.060606..., 1.25, 0, 1, sqrt{5}, pi, e}

Natural: 0, 1

Integers: 0, 1

Rational: -5/3, 2.060606..., 1.25, 0, 1

Irrational: sqrt{5}, pi, e

Real: All the elements in set B are real numbers.

I think this is right.


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#2 2024-09-09 04:12:53

Phrzby Phil
Member
From: Richmond, VA
Registered: 2022-03-29
Posts: 47

Re: Classifying Numbers

There is one more interesting category.

A number is called algebraic if it is the root of a polynomial equation with rational coefficients.

Non-algebraic numbers are called transcendental.

So sqrt(5) is (as you correctly say) irrational, but it is algebraic, being the root of x^2 - 5 = 0.

More complicated to prove: pi and e are not just irrational, but also transcendental.


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#3 2024-09-09 04:58:57

harpazo65
Member
From: Brooklyn, NY
Registered: 2024-09-07
Posts: 52

Re: Classifying Numbers

Phrzby Phil wrote:

There is one more interesting category.

A number is called algebraic if it is the root of a polynomial equation with rational coefficients.

Non-algebraic numbers are called transcendental.

So sqrt(5) is (as you correctly say) irrational, but it is algebraic, being the root of x^2 - 5 = 0.

More complicated to prove: pi and e are not just irrational, but also transcendental.

Interesting facts. I did not know this information.


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